In U.S. Pat. No. 3,317,986 there has been disclosed a ball-bearing assembly with a solid outer race member forming a guide groove for the bearing balls and with an inner race member of mild steel or the like initially forming a seat for these balls in the shape of an annular shoulder, the inner member being subsequently deformed by a punch to convert that seat into another guide groove whereby the two race members are positively interconnected through the intervening balls. Owing to its deformability, the inner race member is more susceptible to wear than would be the case if it could be hardened like the outer one; this drawback can be avoided only through local hardening in the region of the guide groove or raceway, which is a cumbersome and expensive procedure.
It is also known to retain a bearing race in position within a surrounding housing or sleeve, of an axial width slightly exceeding that of the race, by indenting opposite faces of that sleeve near its inner peripheral contact surface in order to upset the edges of that contact surface in a radially inward direction with formation of a pair of lips bracketing the bearing race between them. Such a procedure requires a specific geometric relationship between the hardened structural member and its relatively deformable or upsettable supporting element; thus, it cannot be used where the hardened member has a generally cylindrical surface terminating flush with or extending beyond the corresponding contact surface of the supporting element. Furthermore, the axial forces sustainable by the inwardly upset lips are relatively limited; with castings of light metal or steel of a shear strength below 100 kg/mm.sup.2, these axial forces in kilograms must not exceed 6D in the case of aluminum and steel or about 3D in the case of magnesium alloys, D being the outer diameter of the bearing measured in millimeters. Reference in this connection may be made to the handbook entitled Walzlagerungen by W. Hampp, published by Springer in 1968, pages 91 to 94.